Abstract
Two hierarchies of isospectral and nonisospectral Gerdjikov–Ivanov equations are constructed. Conservation laws of the isospectral soliton hierarchy are explicitly derived from a specific Riccati equation that a ratio of two eigenfunctions satisfies. The corresponding K-symmetries and
τ
-symmetries formulated from the isospectral and nonisospectral hierarchies constitute an infinite-dimensional
τ
-symmetry algebra for the isospectral hierarchy.